dunno, it might still trash 3 coppers the first time you use it. it's not that unlikely. I think the thing with doctor, more than with other cards, is that people have very different ideas about its powerlevel, because it's just so swingy. you might have had a couple of bad games with it, and then stopped buying it for 3$, thus underestimating it now.
but it's not great for 3$. I usually don't like paying 4$ for doctor when opening 3/4$, because you make doctor miss the reshuffle and playing it early is so important with this card, but when there's lookout i might open lookout/doctor for 4$. both of these cards don't trash from your hand, so you should still be able to have enough buying power left to get silvers before your economy is trashed.